Efficient Analog Implementations of Fractional-Order Controllers

Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control applications. It allows to describe dynamical systems more accurately, as well as gain valuable insight into some specific, memory, hereditary, and self-similarity properties of such systems. Fractional-order controllers, e.g. the (PID mu)-D-lambda controller and fractional lead-lag compensator, based on the added flexibility of fractional-order operators, are capable of superior performance compared to their integer-order counterparts. However, there exist multiple issues associated with the implementation of these fractional-order systems. In this work we consider the problem of efficient analog realization of fractional-order controllers. We investigate the possibilities of network generation from fractional-order controller approximations derived using different methods proposed over the years. We consider the problem of practical feasibility of the resulting network as well as the preservation of controller performance specifications. Suitable tools, developed for the MATLAB environment in the context of the FOMCON ("Fractional-order Modeling and Control") toolbox, are presented and discussed. Results of relevant experiments, encompassing the simulation of the designed circuit are provided.